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Emergent Dirac fermions and broken symmetries in confined and deconfined phases of Z2 gauge theories

Nature Physics volume 13, pages 484–490 (2017)Cite this article

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Abstract

Lattice gauge theories are used to describe a wide range of phenomena from quark confinement to quantum materials. At finite fermion density, gauge theories are notoriously hard to analyse due to the fermion sign problem. Here, we investigate the Ising gauge theory in 2 + 1 dimensions, a problem of great interest in condensed matter, and show that it is free of the sign problem at arbitrary fermion density. At generic filling, we find that gauge fluctuations mediate pairing, leading to a transition between a deconfined BCS state and a confined BEC. At half-filling, a π-flux phase is generated spontaneously with emergent Dirac fermions. The deconfined Dirac phase, with a vanishing Fermi surface volume, is a non-trivial example of violation of Luttinger’s theorem due to fractionalization. At strong coupling, we find a single continuous transition between the deconfined Dirac phase and the confined BEC, in contrast to the expected split transition.

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Figure 1: Schematic phase diagram at fixed μ > 0 as a function of h/J and the temperature T for the ‘even’ sector of the gauge theory.
Figure 2: Schematic T = 0 phase diagram at half-filling μ = 0, with a novel, deconfined Dirac semi-metal at large fermion hopping t.
Figure 3: QMC results for confinement and superconductivity as a function of h at J = 1, t = 0.5, μ = 0.3 on L × L lattices at temperature T = 1/β.
Figure 4: The evolution from a deconfined BCS state to a deconfined Dirac phase with increasing t in the weak coupling regime J = 0.3 h = 0.1.
Figure 5: Phase transition from a confined BEC to a deconfined Dirac phase driven by increasing t at μ = 0 with J = 0.1, h = 0.2.
Figure 6: Finite size scaling analysis of the phase transition between a confined BEC/CDW and a deconfined Dirac phase driven by increasing h at μ = 0 with J = −1, t = 1.0.

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Acknowledgements

We thank S. Sachdev and T. Senthil for discussions. S.G. was supported by the Simons Investigators Program, the California Institute of Quantum Emulation and the Templeton Foundation. M.R. acknowledges support from NSF DMR-1410364 and the hospitality of the Berkeley CMT Group in Fall 2015. A.V. acknowledges support from the Templeton Foundation and a Simons Investigator Award. Part of this work was performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293. This research was done using resources provided by the Open Science Grid45,46, supported by the NSF, and used the Extreme Science and Engineering Discovery Environment47 (XSEDE), supported by NSF grant ACI-1053575.

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Authors and Affiliations

  1. Department of Physics, University of California, Berkeley, California 94720, USA

    Snir Gazit & Ashvin Vishwanath

  2. Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA

    Mohit Randeria

  3. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    Ashvin Vishwanath

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  1. Snir Gazit
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S.G. conceived of and carried out the numerical simulations and data analysis. All authors contributed to the development of the theoretical results and to the writing of the manuscript.

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Correspondence to Snir Gazit.

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Gazit, S., Randeria, M. & Vishwanath, A. Emergent Dirac fermions and broken symmetries in confined and deconfined phases of Z2 gauge theories. Nature Phys 13, 484–490 (2017). https://doi.org/10.1038/nphys4028

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